Physics 110
Name
Lab #7: Transverse Standing Waves
1
Introduction
When an object travels it carries along energy and momentum, because it has mass. In a traveling wave
energy and momentum are made to travel in space, in the absence of the transmission of any mass. This is
because in wave motion it is the ‘disturbance’ that moves. But like objects (particles), waves exhibit many
physical phenomena such as transmission, reflection, energy loss, etc. They also exhibit phenomenon very
different from particles. One of these is that of interference: two waves that travel in opposite directions pass
through each other so that at every point in space the net disturbance is an effective sum of their individual
disturbances.
In this laboratory an example of standing waves, waves created when two traveling waves interfere in just
the right way (‘resonance’) to produce a stationary pattern of nodes (places of zero wave disturbance) and
antinodes (places of maximal disturbance).
For the one dimensional systems we will study in this lab, a simple relation exists connecting the distance
between successive nodes, the frequency of the driving mechanism, and the speed of wave propagation in the
medium of interest:
vwave = f λ
where vwave is the wave propagation speed, λ is the wavelength of the standing wave (which equals twice
the distance between successive nodes; why?), and f is the (resonant) frequency of the standing wave.
2
Transverse waves on a String
1. Measure the mass and length of the string, removing all knots.
2. Set up the string with a 200g mass hung over the pulley and measure and record the length of the
string between the two fixed nodes (that at the pulley and that at the mechanical oscillator). Carefully
adjust the frequency of the driver so that resonances are formed with 1 to at least 7 loops. Record the
frequencies (make two measurements at each resonance and report the average) and sketch the loop
structure in each case. Are the resonant frequencies equally spaced?
3. Determine how to plot your resonant frequency and λ data so that a linear plot results, with slope
equal to vwave . Make and attach your plot and record vwave .
4. The wave velocity can also be found from the equation
vwave =
s
FT
µ
where T is the tension in the string and µ is the linear mass density of the string (= mass/length). Use
your values of the mass and length to determine µ and then compute a velocity using this equation:
5. Write a paragraph, comparing your two values of the velocity. Identify systematic effects which might
account for a difference.